Strength of Materials - B.Tech 4th Semester Examination, 2022

Two parallel, equal and opposite forces acting tangentially to the surface of the body is called

1. complementary stress
2. compressive stress
3. shear stress
4. tensile stress

Maximum shear stress is

1. average sum of principal stresses
2. average difference of principal stresses
3. average sum as well as difference of principal stresses
4. None of the above

What will be the radius of gyration of a circular plate of diameter \( 10 \text{ cm} \)?

1. \( 2.5 \text{ cm} \)
2. \( 2.0 \text{ cm} \)
3. \( 1.5 \text{ cm} \)
4. \( 3 \text{ cm} \)

Which of the following are statically determinate beams?

1. Only simply supported beams
2. Continuous beams
3. Fixed beams
4. Cantilever, overhanging and simply supported beams

In a cantilever carrying uniformly varying load starting from zero at the free end, the bending moment diagram

1. is a horizontal line parallel to x-axis
2. is a line inclined to x-axis
3. follows a parabolic law
4. follows a cubic law

Calculate the deflection if the slope is \( 0.0225 \text{ radians} \). Take the distance of centre of gravity of bending moment to free end as 2 metres.

1. \( 45 \text{ mm} \)
2. \( 35 \text{ mm} \)
3. \( 28 \text{ mm} \)
4. \( 49 \text{ mm} \)

Hoop stress in a thin vessel is

1. \( pD/4t \)
2. \( pD/2t \)
3. \( pD/3t \)
4. None of the above

Hoop shrinking in thick cylinders is done to achieve

1. increased stresses
2. decreased stresses
3. uniform stresses
4. None of the above

Two shafts in torsion will have equal strength if

1. only diameter of the shafts is same
2. only angle of twist of the shaft is same
3. only material of the shaft is same
4. only torque transmitting capacity of the shaft is same

What is the maximum principal stress induced in a solid shaft of \( 40 \text{ mm} \) diameter which is subjected to both bending moment and torque of \( 300 \text{ kN-mm} \) and \( 150 \text{ kN-mm} \) respectively?

1. \( 50.57 \text{ N/mm}^2 \)
2. \( 28.1 \text{ N/mm}^2 \)
3. \( 21.69 \text{ N/mm}^2 \)
4. \( 52.32 \text{ N/mm}^2 \)

Derive the relation between \( E \) and \( K \). A bar of \( 30 \text{ mm} \) diameter is subjected to a pull of \( 60 \text{ kN} \). The measurement extension on gauge length of \( 200 \text{ mm} \) is \( 0.1 \text{ mm} \) and change in diameter is \( 0.004 \text{ mm} \). Calculate \( E \), Poisson ratio and \( K \).

Three bars made of copper, zinc and aluminium are of equal length and have cross-section \( 500 \), \( 700 \) and \( 1000 \text{ mm}^2 \) respectively. They are rigidly connected at their ends. If this compound member is subjected to a longitudinal pull of \( 250 \text{ kN} \). Estimate the proportional of the load carried on each rod and the induced stresses. Take the values of \( E \) for copper \( = 1.3 \times 10^5 \text{ N/mm}^2 \) and for zinc \( 1.0 \times 10^5 \text{ N/mm}^2 \) and for aluminium \( = 0.8 \times 10^5 \text{ N/mm}^2 \).

A material is subjected to two mutually perpendicular tensile direct stresses of \( 40 \text{ MPa} \) and \( 30 \text{ MPa} \) together with a shear stress of \( 20 \text{ MPa} \), shear stress being clock-wise on the face carrying the \( 40 \text{ MPa} \) tensile stress. Determine-
(a) the stresses on a plane making an angle of \( 40^{circ} \) counter-clockwise to the plane of the \( 40 \text{ MPa} \) stress;
(b) the principal stresses and their planes;
(c) the maximum shear stress and its plane.

With the help of mathematical proof, show that the torque transmitted by the hollow shaft is greater than the solid shaft.

A hollow shaft with diameter ratio \( 3/5 \) is required to transmit \( 450 \text{ kW} \) at \( 120 \text{ r.p.m.} \) The shearing stress in the shaft must not exceed \( 60 \text{ N/mm}^2 \) and the twist in a length of \( 2.5 \text{ m} \) is not to exceed \( 1^{circ} \). Calculate the minimum external diameter of the shaft. Take \( C = 80 \text{ kN/mm}^2 \).

A simply supported beam is subjected to a combination of loads as shown in Fig. 1. Sketch the shear force and bending moment diagrams and find the position and magnitude of maximum bending moment.

Derive expression for moment of inertia for circular lamina and thin ring.

Determine the moment of inertia of the beam cross-section about the centroidal axis shown in Fig. 2.

Derive the expression for the change in diameter and for the change in volume of a thin spherical shell when it is subjected to an internal pressure.

A thin cylinder is \( 3.5 \text{ m} \) long, \( 90 \text{ cm} \) in diameter, and the thickness of the metal is \( 12 \text{ mm} \). It is subjected to an internal pressure of \( 2.8 \text{ N/mm}^2 \). Calculate the change in dimensions of the cylinder and the maximum intensity of shear stress induced. \( E = 200 \text{ GPa} \) and Poisson's ratio \( = 0.3 \).

Calculate circumferential and radial stress in a thick cylinder assuming internal pressure \( p_i \) and internal pressure = zero.

An external pressure of \( 10 \text{ MN/m}^2 \) is applied to a thick cylinder of internal diameter \( 160 \text{ mm} \) and external diameter \( 320 \text{ mm} \). If the maximum hoop stress permitted on the inside wall of the cylinder is limited to \( 30 \text{ MN/m}^2 \), what maximum internal pressure can be applied assuming the cylinder has closed ends? What will be the change in outside diameter when this pressure is applied? \( E = 207 \text{ GN/m}^2 \), \( v = 0.29 \).

Deduce the expression for bending equation. What is section moduli of hollow circular section and solid circular section?

A simply supported beam is subjected to uniformly distributed load in combination with couple \( M \). It is required to determine the deflection shown in Fig. 3.